Groups acting properly on "bolic" spaces and the Novikov conjecture

2004/02/23 by Gennadi Kasparov, Georges Skandalis · 2 citations
Mathematics · #math.AG

paper · pdf

published as Ann. of Math. (2), Vol. 158 (2003), no. 1, 165--206 · 42 pages, published version

arxiv created 2004/02/23 · arxiv updated 2009/12/01

Abstract

We introduce a class of metric spaces which we call "bolic". They include hyperbolic spaces, simply conneccted complete manifolds of nonpositive curvature, euclidean buildings, etc. We prove the Novikov conjecture on higher signatures for any discrete group which admits a proper isometric action on a "bolic", weakly geodesic metric space of bounded geometry.

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